The Crusaders' plan was to use Italian ships to transport their army to Egypt and to conquer their way to Jerusalem from there. So, they sent envoys to the various Italian city states to procure a navy for the expedition. Everyone but the Venetians said no, and thus the envoys arranged for the Venetians to constructed a massive navy to accommodate the 35,000+ troops who they expected to make up the crusading army, payment due when the army arrived. Thanks to the dissension which was all too common in Crusading armies there were any number of delay, defections, and nobles with their own idea of how and where the Crusaders should leave from resulting in about 1/3 of the expected number actually showing up in Venice. This understandably irritated the Venetians who expected to be paid for the huge, economy crippling, number of ships which they had built.

After quite a bit of hemming and hawing, the Crusaders agreed to raid up and down the Dalmatian coast for the Venetians, culminating in attacking the Hungarian city of Zara, which resulted in the excommunication of the Crusade and further defections as many leaders simply refused to participate. The Crusaders end up spending the winter in Zara, when along comes Alexios IV, the son of the recently deposed Emperor Isaac II. Alexios starts making all sorts of grand promises to the Crusaders, that he'd pay all their debts, that he'd reunite the Eastern and Western Churches under the control of the Pope, that he'd give them all sorts of resources to further the Crusade, and more if the Crusaders would help him gain the throne. There's pretty much no chance he would actually have been able to fulfill these promises, and how aware of this the Crusaders were is up for debate. From what I've seen the general consensus is that the Venetians certainly knew that it was nonsense, but they'd had all sorts of problems with Constantinople, rivals for control of the eastern Mediterranean, in the recent past, so were well disposed to exacting some revenge and increasing their power as a means of salvaging what was a pretty disastrous campaign thus far.

So, the Crusaders head to Byzantium, defeat Angelos III, and place Alexios IV's father, Isaac II< back on the throne with Alexios alongside him as co-emperor. There're some scuffles between the Crusaders and Greeks, leading to a huge chunk of Constantinople being burnt down, followed shortly after by Isaac II dying and Alexios pissing off just about everyone who matters (including the Crusaders because, surprise surprise, he can't pay), leading to the coronation of a rival emperor (Alexios V) who promptly defeats and murders Alexios IV. The Crusaders, still looking for their money and miffed that he murdered their supposed patron demand that Alexios V pay them what was promised by his predecessor. When he refuses, they attack the city, Alexios V flees, and the Sack of Constantinople follows soon after.

Geoffrey of Villehardouin was a first-hand participant in the Crusade and wrote an account which lays out the whole disaster in detail.